Question

what is the largest perimeter of an isosceles triangle with side lengths of 30 and 40?
your answer
largest: 4, 9 *
your answer
smallest: 9, 4 *
your answer
what is the smallest perimeter of an isosceles triangle with side lengths of 30 and 40?
your answer

Explanation:

Step1: Check triangle inequality for two cases

Case1: Sides \(30,30,40\). Check \(30 + 30>40\) (True), \(30+40 > 30\) (True), \(40 + 30>30\) (True). Perimeter \(P_1=30 + 30+40=100\).
Case2: Sides \(40,40,30\). Check \(40 + 40>30\) (True), \(40+30 > 40\) (True), \(30 + 40>40\) (True). Perimeter \(P_2=40 + 40+30=110\).

Step2: Compare perimeters

Since \(110>100\).

Answer:

The largest perimeter is \(110\).

Step1: For the smallest perimeter (already considered in previous step)

We have two cases. As shown above, perimeter \(P_1 = 100\) (from sides \(30,30,40\)) and \(P_2=110\) (from sides \(40,40,30\)).